Trignometry Question Please help

Answer:

C. Rectangle ABCD was dilated with center (0, 0) and a scale factor of 1/2 followed by a translation right 3.5 units and down 8 units.

Step-by-step explanation:

See figure for intermediate steps.

The transformed rectangle ABCD was dilated with center (0, 0) and a scale factor of 1/2 followed by a translation right 3.5 units and down 8 units.

The transformation of a function may involve any change.

Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs), etc.

If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:

Horizontal shift (also called phase shift):

Left shift by c units: y=f(x+c) (same output, but c units earlier)

Right shift by c units: y=f(x-c)(same output, but c units late)

Vertical shift:

Up by d units: y = f(x) + d

Down by d units: y = f(x) - d

Stretching:

Vertical stretch by a factor k: y = k × f(x)

Horizontal stretch by a factor k: y = f(x/k)

Given data ,

Let the rectangle be represented as ABCD

Now , the coordinates of the rectangle are

A ( 1 , 9 ) , B ( 1 , 6 ) , C ( 7 , 6 ) and D ( 7 , 9 )

Now , the rectangle is dilated with scale factor of 1/2 , we get

A ( 0.5 , 4.5 ) , B ( 0.5 , 3 ) , C ( 3.5 , 3 ) and D ( 3.5 , 4.5 )

And , the rectangle is translated right 3.5 units and down 8 units.

So , the new coordinates of the rectangle is

E ( 4 , -3.5 ) , F ( 4 , -5 ) , G ( 7 , -5 ) and H ( 7 , -3.5 )

Hence , the transformed rectangle is E ( 4 , -3.5 ) , F ( 4 , -5 ) , G ( 7 , -5 ) and H ( 7 , -3.5 )

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Answer:

A, E, F, G

Step-by-step explanation:

The picture below represents a parabolic arc.

An example can be an object being thrown up in the air then then coming back down.

Answer:

The answer is A.

Step-by-step explanation:

So we have the two equations:

[tex]3x+y=1\\y+4=5x[/tex]

To make a substitution of the second equation into the first equation, we need to isolate the y variable in the second equation. Thus:

[tex]y+4=5x\\y=5x-4[/tex]

Now, we can substitute this into the first equation. Therefore:

[tex]3x+y=1\\3x+(5x-4)=1\\3x+5x-4=1[/tex]

Answer:

[tex]\large \boxed{\sf \ \ 70\% \ \ }[/tex]

Step-by-step explanation:

Hello,

We assume that the year is 52 weeks, and we note r the interest rate we are looking for. The rate is expressed in percent and is annually, meaning that the investment is, after the first week :

   [tex]1000\cdot (1+\dfrac{r\%}{52})=1000\cdot (1+\dfrac{r}{5200})[/tex]

For the second week

   [tex]1000\cdot (1+\dfrac{r}{5200})^2[/tex]

After 52 weeks

   [tex]1000\cdot (1+\dfrac{r}{5200})^{52}[/tex]

and we want to be equal to 2000 so we need to solve:

[tex]1000\cdot (1+\dfrac{r}{5200})^{52}=2000\\\\\text{*** divide by 1000 both sides ***}\\\\(1+\dfrac{r}{5200})^{52}=\dfrac{2000}{1000}=2\\\\\text{*** take the ln **}\\\\52\cdot ln(1+\dfrac{r}{5200})=ln(2)\\\\\text{*** divide by 52 ***}\\\\ln(1+\dfrac{r}{5200})=\dfrac{ln(2)}{52}\\\\\text{*** take the exp ***}\\\\\displaystyle 1+\dfrac{r}{5200}=exp(\dfrac{ln(2)}{52})=2^{(\dfrac{1}{52})}=\sqrt[52]{2}\\\\r = 5200\cdot (\sqrt[52]{2}-1)=69.77875...[/tex]

Rounded to the nearest percent, the solution is 70%.

If you want to double your capital in one year with weekly compounding you need an interest rate of 70% !!

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

4%

Step-by-step explanation:

Answer:

The first way to prove that the diagonals of a rectangle are congruent is to show that triangle ABC is congruent to triangle DCB

Here is what is given: Rectangle ABCD

Here is what you need to prove: segment AC ≅ segment BD

Since ABCD is a rectangle, it is also a parallelogram.

Since ABCD is a parallelogram, segment AB ≅ segment DC because opposite sides of a parallelogram are congruent.

Step-by-step explanation:

Given:

x = 26214.47

s = 5969.25

n = 15

t = 2.046

The confidence interval is:

CI = x ± t (s / √n)

CI = 26214.47 ± 2.046 (5969.25 / √15)

CI = (23061.06, 29367.88)

Answer:

C.  6√5

Step-by-step explanation:

√20 +√80= √4*5 + √16*5 = 2√5 + 4√5 = 6√5

Answer:

140 poles

Step-by-step explanation:

1. Convert to the same unit. Either meters to kilometers or kilometers to meters, so you can complete the computation.

2. Divide 0.06 by 8.4 (8.4/0.06 = 140).

3. 140 poles can be placed on the 8.4 km road when separated by 60 m or 0.06 km.

Answer:

The value of the exponent of the base 10 for this product is -2.

Step-by-step explanation:

[tex]5.86\,\,10^{-7}\,\,*\,\,3.1\,\,10^4=18.166\,\,10^{-7+4}=18.166\,\,10^{-3}[/tex]

Now, in order to represent this number in scientific notation, we need to reduce the coefficient 18.166 to a coefficient larger or equal to 1 and smaller strictly than 10, by using division or multiplications by powers of 10. In order to reduce it to 1.8166, we need to divide the original 18.166 by ten so we do the following in order not to change the given number (multiply and divide by ten at the same time):

[tex]\frac{18.166\,\,10}{10} \,10^{-3}=1.8166\,*\,10\,*\,10^{-3}=1.8166\,\,10^{-2}[/tex]

Answer:

-2

Step-by-step explanation:

1. Write the expression:       (5.86 × 10–7)(3.1 × 104)

2. Rearrange the expression:     (5.86 × 3.1)(10–7 ∙ 104)

3. Multiply the coefficients:      (18.166)(10–7 ∙ 104)

4. Apply the product of powers:    18.166 × 10-3

5. Write in scientific notation:     1.8166 × 10n

do all this get negitive two

Answer:

false!

Step-by-step explanation:

i just answered true and it was false. so false is correct!

The statement that the horizontal cross-sectional shapes of the given prism are all congruent is false.

Prisms are three-dimensional shapes that have its two ends to be parallel and congruent

The given prism is a trapezoidal prism.

For the horizontal sectional shapes given prism to be congruent, the prism must be cut through the middle

Since the prism can be divided at any point, then the given statement is false

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Answer:

(-3, 3.25)

Step-by-step explanation:

Answer:

2 ¹/12

Step-by-step explanation:

convert 1 4/12 to an improper fraction

(1×12+4)=16/12

16/12+9/12=25/12

convert 25/12 to a mixed fraction

=2 ¹/12

Divide the largest one by the smallest one : for example, the number 4 is 42=2× larger than the number 2.

Indeed, If you multiply 2 by 42 you'll get 4.

Of course, if a number is n× larger than another, then this other is n× smaller than the first one.

It will of course work with floating point : 0.6×10.6≈0.6×1.6667=1 so 1 is ~1.6667 times larger than 0.6 while 0.6 is ~1.6667 smaller than 1.

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Answer:

3/8

Step-by-step explanation:

If 5/8 of the staff is male, then 8/8 is the total number of staff.

8/8 - 5/8 = 3/8

3/8 of the staff is female.

Hope this has helped. If the question has more to it, then please specify.

Answer:

The answer is

Step-by-step explanation:

The distance between two points is found by using the formula

[tex] \sqrt{ {(x1 - x2)}^{2} + {(y1 - y2)}^{2} } [/tex]

Where (x1 , y1) and ( x2 , y2) are the points

The distance between (-6, -2) and (0, -1) is

[tex] \sqrt{ {( - 6 - 0)}^{2} + {( - 2 + 1)}^{2} } \\ \\ = \sqrt{ {( - 6})^{2} + {( - 1)}^{2} } \\ \\ = \sqrt{36 + 1} \\ \\ = \sqrt{37} \: units[/tex]

Hope this helps you

Answer: √37 units

hope that helped!

Answer:

[tex]Volume = 1017.36\ in^3[/tex] -- Cone

[tex]Volume = 3052.08\ in^3[/tex] -- Cylinder

[tex]Volume = 3052.08\ in^3[/tex] -- Sphere

Best Buy: Sphere Clay

Step-by-step explanation:

Given

Solid Shapes: Cone, Cylinder, Sphere

Cost of Cone Clay = $12

Cost of Cylinder Clay = $30

Cost of Sphere Clay = $28

Required

Determine the volume of each shape

Which is the best buy

The volume of a cone is calculated as thus;

[tex]Volume = \frac{1}{3}\pi r^2h[/tex]

From the attached diagram

Radius, r = 9 inches; Height, h = 12 inches and [tex]\pi = 3.14[/tex]

Substitute these values in the above formula;

[tex]Volume = \frac{1}{3} * 3.14 * 9^2 * 12[/tex]

[tex]Volume = \frac{3052.08}{3}[/tex]

[tex]Volume = 1017.36\ in^3[/tex]

The unit cost of the cone is calculated as thus;

[tex]Volume:Price = \frac{Volume}{Total\ Cost}[/tex]

Where

[tex]Volume = 1017.36\ in^3[/tex]

[tex]Total\ Cost = \$12[/tex] (Given)

[tex]Volume:Price = \frac{1017.36\ in^3}{\$ 12}[/tex]

[tex]Volume:Price = 84.78 in^3/\$[/tex]

[tex]Volume:Price = 84.78 in^3:\$1[/tex]

The volume of a cylinder is calculated as thus;

[tex]Volume = \pi r^2h[/tex]

From the attached diagram

Radius, r = 9 inches; Height, h = 12 inches and [tex]\pi = 3.14[/tex]

Substitute these values in the above formula;

[tex]Volume = 3.14 * 9^2 * 12[/tex]

[tex]Volume = 3052.08\ in^3[/tex]

The unit cost of the cone is calculated as thus;

[tex]Volume:Price = \frac{Volume}{Total\ Cost}[/tex]

Where

[tex]Volume = 3052.08\ in^3[/tex]

[tex]Total\ Cost = \$30[/tex] (Given)

[tex]Volume:Price = \frac{3052.08\ in^3}{\$ 30}[/tex]

[tex]Volume:Price = 101.736\ in^3/\$[/tex]

[tex]Volume:Price = 101.736\ in^3:\$1[/tex]

The volume of a sphereis calculated as thus;

[tex]Volume = \frac{4}{3}\pi r^3[/tex]

From the attached diagram

Radius, r = 9 inches; and [tex]\pi = 3.14[/tex]

Substitute these values in the above formula;

[tex]Volume = \frac{4}{3} * 3.14 * 9^3[/tex]

[tex]Volume = \frac{9156.24}{3}[/tex]

[tex]Volume = 3052.08\ in^3[/tex]

The unit cost of the cone is calculated as thus;

[tex]Volume:Price = \frac{Volume}{Total\ Cost}[/tex]

Where

[tex]Volume = 3052.08\ in^3[/tex]

[tex]Total\ Cost = \$28[/tex] (Given)

[tex]Volume:Price = \frac{3052.08\ in^3}{\$ 28}[/tex]

[tex]Volume:Price = 109.003\ in^3/\$[/tex]

[tex]Volume:Price = 109.003\ in^3:\$1[/tex]

Comparing the Volume:Price ratio of the three clay;

The best buy is the sphere because it has the highest volume:price ratio.

Having the highest volume:price ratio means that with $1, one can get more clay from the sphere compared to other types of clay

Answer:

241 mm^2.

Step-by-step explanation:

There are 10 mm in a cm so there are 10*10 = 100 mm^2 in  a cm^2.

So the answer is 2.41 * 100 = 241 mm^2.

Answer:

241mm²

Step-by-step explanation:

If 10mm = 1cm,

then 100mm² = 1cm²

2.41 × 100 = 241mm²

Answer:

See below.

Step-by-step explanation:

To find the equation, we need to find the slope and the y-intercept. Afterwards, we can put the numbers into the slope-intercept form:

[tex]y=mx+b[/tex]

From the graph, we can see that the line crosses the y-intercept at y=-6. Thus, the y-intercept (b) is -6.

Now we need to find the slope. Pick any two points where the line crosses. I'm going to pick (0,-6) and (4,-7).

[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{-7-(-6)}{4-0}= -1/4[/tex]

Therefore, the equation of the line would be:

[tex]y=mx+b\\y=-1/4x-6[/tex]

Answer: the answer would be 24

Step-by-step explanation: just did the assignment

Answer:

24

Step-by-step explanation:

Just got it right on edge 2020

Answer:

x = -5.

Step-by-step explanation:

The solutions of the equation is when the two functions intersect. That is at (-5, 5.5), so where x = -5.

Hope this helps!

Answer:

x = -5

Step-by-step explanation:

f(x) = g(x) has more than one solution, because they intersect at two points.

The question asks for one solution of f(x) = g(x).

One point where they intersect is at (-5, 5.5), as shown in the graph.

(x , y)

x = -5, y = 5.5

Answer:

Step-by-step explanation:

In order to convert a binary number into a decimal, it is expanded in the power of 2. Then, by simplifying the expanded form of the binary number, we obtain a decimal number.

Let's solve:

[tex]1000110[/tex]

[tex] = 1 \times {2}^{6} + 0 \times {2}^{5} + 0 \times {2}^{4} + 0 \times {2}^{3} + 1 \times {2}^{2} + 1 \times {2}^{1} + 0 \times {2}^{0} [/tex]

[tex] = 1 \times 64 + 0 \times 32 + 0 \times 16 + 0 \times 8 + 1 \times 4 + 1 \times 2 \times 0 \times 1[/tex]

[tex] = 64 + 0 + 0 + 0 + 4 + 2 + 0[/tex]

[tex] = 70[/tex]₁₀

Hope I helped!

Best regards!!

Answer:

k=4

Step-by-step explanation:

We can use the slope formula

m = (y2-y1)/(x2-x1)

-2 = (k-2)/(-4 - -3)

-2 = (k-2)/(-4+3)

-2 = (k-2)/ ( -1)

Multiply by -1

-2 * -1 =  (k-2)/ ( -1) * -1

2 = k-2

Add 2 to each side

2+2 = k-2+2

4 =k

Answer:

125 : 729

Step-by-step explanation:

Given the ratio of the radii of 2 similar spheres = a : b , then

ratio of volumes = a³ : b³

Here the ratio of radii = 5 : 9 , thus

ratio of volumes = 5³ : 9³ = 125 : 729

Answer:

the ansewr is b

Step-by-step explanation:

Answer:

C. The hypotenuse is [tex]\sqrt{2}[/tex] times as long as either leg.

Step-by-step explanation:

The hypotenuse is square root 2 times as long as the sides is a true statement.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

We have to find the true statement about an isosceles right triangle.

Let us use pythagoras theorem to find this

h²=a²+b²

In this case since its an isosceles right triangle, a and b most be the same.

Let's say that the measure of the sides that are equal is x and the hypotenuse is h.

Pythagoras tells us the following:

h²=x²+x²

h²=2x²

Take square root on both sides

h=√2x

Hence, the hypotenuse is square root 2 times as long as the sides

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Answer:

[tex]7\sqrt{2}[/tex]

Step-by-step explanation:

Use trigonometry.

sin 45 degrees = x/14

plug in values and you get x = [tex]7\sqrt{2}[/tex]

Answer:

72

Step-by-step explanation:

Answer:

La respuesta es 7+6 ó 6+7 que es 13

Answer:

12.5%

Step-by-step explanation:

The price for the ski = $2000

The payments made each = $250

percentage of the total cost that the payment is = ?

The percentage will be calculated as

the ratio of the payments made to the price of ski times 100%

250/2000 x 100%

==> 0.125 x 100% = 12.5%

Answer:

6.09

Step-by-step explanation:

in ADB

[tex]a ^{2} + b^{2} = c ^{2} [/tex]

to get hypotenuse=8.96

this is height of ABC so use tan

[tex] tan(55.8)= 8.96 \x[/tex]

x=6.09

Answer:

D

Step-by-step explanation:

To find x, we first to to find the line between A&B.

Use the pythagoram theorem to do this A^2+B^2=C^2

4.9^2+7.5^2=C^2

80.26=C^2

square root each side

Side AtoB=8.958

We now know the side length of the opposite and adjacent for the angle C. So according to SohCahToa we need to use Tangent.

So Tan(55.8)=(8.958/x)

We you solve for x, the answer is 6.088

Step-by-step explanation:

Notice how you get the same value each time when you divide the cost by the number of downhill rides

Moreover when the downhill rides grow by 2 the total cost grows by 5

so we can state :

To complet the chart we can use the proportionaliyu relation:

so 20 goes with 50

same method:

so 25 goes with 62.5